A Global Coupled Atmosphere-Wave Model System Based on C-Coupler2. Part I: Model Description

This study presents a global coupled atmosphere-wave model system (MPAS-NWW3) and its verification. The Community Coupler2 (C-Coupler2), a developed coupler, is used to couple the global wave configuration of the NWW3 (WAVEWATHCH III) with the global atmosphere configuration of the MPAS-Atmosphere model. Surface wind at 10 meters above sea level, temperature and specific humidity at 2 meters above sea level are the coupled variables for atmospheric component model, and significant wave height, average wave length and peak frequency are for wave component model. Some codes are added to the surface layer scheme and the effect of momentum flux induced by sea waves is taken into consideration in this paper. All the coupled variables, input or output the coupler are demonstrated their consistency in the MPAS-NWW3 coupled model.


Introduction
As is well known, coupling between various models, such as atmospheric, waves, oceanic, and land models, could improve the predictions of atmospheric and oceanic states involving different time scales [1][2].With the increasing capabilities of computational resources, the application of coupling allows the increased model complexity.
Over the past few decades, numerous coupled models that consist of atmosphere, wave and ocean models have been developed.It has been shown in many studies that wave processes or the sea surface temperature can affect the roughness or heat fluxes at air-sea surface, thereby improving the accuracy of numerical weather prediction [3][4].There have been developed many fully coupled models (coupled with atmospheric, waves, oceanic models), with the goal of simulating air-sea interactions and implementing for the simulation of extreme events or operational forecasts.Most coupled atmosphere-ocean or atmosphere-wave-ocean models were interested in the air-sea interaction, particularly the change of SST or heat fluxes, and were mostly focused on the tropical cyclone forecasting or discussion on a decadal timescale [5][6][7][8].For example, the tropical cyclone simulation has been carried out using the COAWST modeling system [5][6].Traditional standalone atmospheric model usually uses idealized parameters in surface layer during the forecast process, but in the simulation of coupled models, the influence of wind wave and swell wave on the accuracy of prediction was the main research direction [7].Most coupled models are applied to regional scale or climate models, despite the fact that they are currently being implemented with more complicated physical processes and higher temporal or geographical resolution.Few coupled atmosphere-wave model exists on a global scale, and even fewer on the synoptic scale.
The atmospheric model, Model for Prediction Across Scales-Atmosphere (MPAS-A), and the wave model, the Third Generation Wave Model, WAVEWATHCH III (NWW3), have been coupled in this study using the Community Coupler2 (C-Coupler2), an efficient coupling framework [8].After the development of global coupled MPAS-NWW3 system, case studies were run and verification procedures were carried out to demonstrate that the coupler can effectively transfer and interpolate the coupled variables.
In this article, the stress describes the strategies of coupled MPAS-NWW3 model and verification of variables consistency in it.The paper is presented in four sections.Section 2 provides a full overview of the coupled MPAS-NWW3 model and its techniques.In section 3, we check the coupled model's variables for consistency.A summary and outlook for future work are concluded in the last section.

The atmospheric component model
The atmospheric component model used in this study is MPAS-A v5.2, Model for Prediction Across Scales-Atmosphere.Collaboratively developed by NCAR and LANL, MPAS-A is a global completely compressible nonhydrostatic model with finite-volume numerics discretized on centroidal Voronoi meshes employing C-grid staggering of the prognostic variables.Similar to icosahedral meshes, quasiuniform centroidal Voronoi meshes offer almost uniform resolution on global scale.Distributedmemory parallelism is more effective when compared to the conventional equidistant longitudelatitude grids because unstructured Voronoi meshes, or officially SCVTs, scale well on supercomputers that depend on numerous distributed-memory processing elements [9].MPAS-A model is widely used in the global atmospheric numerical simulation now [10], and the latest version includes the capability to perform regional simulations.

The wave component model
The wave component model used in the coupled model is the Third-Generation Wave Model, WAVEWATHCH III (NWW3 v4.18), developed by NOAA and NCEP [11].NWW3 takes into account some elements such as the wind input, white-capping-related dissipation, wave-bottom contact and wave-wave interaction [12].The NWW3 model is widely used in the regional or global simulation of nearshore wave, storm wave [13][14].The mesh structure of the NWW3 model is equidistant latitude and longitude grid with the specific horizontal resolution.Due to the characteristics of the mesh, it is easy for the model to generate instability near the pole region and at high latitude.

The coupler component model
C-Coupler2, the 2.0 version of C-Coupler developed at Tsinghua University, has following outstanding advantages: 1) the flexible coupling configuration interfaces, including coupling frequencies and model grids; 2) automatic coupling processing like data interpolation; 3) dynamic three-dimensional coupling capability; 4) promote model nesting and incremental operation; 5) capability of adaptive restart capability.C-Coupler2 has been applied in a few coupled models and coupled ensemble data assimilation [2] [15].
Owing to the difference between the centroidal Voronoi meshes (nominally hexagon) and latitudelongitude grid, applied in MPAS-A and NWW3 respectively, C-Coupler2 plays a significant role in the coupled model to accomplish data transfer and data interpolation on specific coupling frequencies.

Coupling strategy
The C-Coupler2 bidirectional transfers variables between MPAS-A and NWW3 as a library (Figure 1).The coupling frequency is set to time step in each component, which indicates that the coupled variables are exchanged at that time-step.It should be mentioned here that the coupler sends the coupled variables of MPAS-A to NWW3 at the initial time to drive the NWW3 model.The MPAS-A model sends coupled variables, including surface wind at 10 meters above sea level, temperature and specific humidity at 2 meters above sea level to coupler, and the coupled variables directly drive the wave component model.At the same time, NWW3 sends significant wave height, average wave length and peak frequency back, and MPAS-A receives these coupled variables to calculate an improved sea surface roughness.In this study, only the change in momentum flux brought on by the sea wave is considered in atmospheric model, the heat flux is not taken into account.
The coupler is crucial in the coupled model since MPAS-A's mesh structure and domain differ from those of NWW3 model.According to Figure 2, each component model's domain is distinct, and the domain of NWW3 is smaller than that in MPAS-A.The C-Coupler2 uses bilinear interpolation (inside the model mesh) and extrapolation (close to the mesh boundary) method to distinguish land and sea distribution.Model mesh structure is the basis of interpolation calculation and variable storage.The exchange of variables between each component model in MPAS-NWW3 coupled system occurs in a two-dimensional horizontal mesh because only variables on sea level are involved.Interpolation between the component models in various mesh structures is the other significant job of coupler.It helps each component model recognize the coupled variables.Additionally, the coupler completes the mesh parallel subdivision to achieve model integration acceleration on high-performance computers.The surface layer scheme in traditional MPAS-A model uses the classic Charnock method to determine the surface roughness [16], whose formula is shown in (1): In formula (1), 0 z is the roughness length on sea surface, β is the Charnock coefficient, which is 0.016 in formula, * u is the friction velocity, g is gravitational constant.According to this method of computation, the surface roughness length was only related to the surface wind.Other influencing factors, such as the dependence of sea waves, were not taken into account.
Here, we add a few algorithms to make it possible for the MYNN surface layer scheme to change in response to sea wave effects.Based on Taylor and Yelland [23], the first method considers the influence of wave steepness, and the formula for computation is displayed in (2): ( ) H means the significant wave height, p L is the mean wave length,  is the kinematic viscosity ( 2 -1 m s ) based on Andreas (1989).The second method considers the effect of wave age based on Drennan [17] and the formula is shown as (3): where p C represents wave phase speed at the peak of the spectrum, and * p uC means the parameter of wave age.The third method considers dependence of roughness length on both wave age and wave steepness based on Oost et al. [18], and as shown in the formula (4): ( ) In the previous researches, different coupling techniques demonstrated varying degrees of inhibition on the surface roughness and surface wind.In this work, the first coupled technique which considers the relationship between the surface roughness and wave steepness was primarily examined.Future studies will examine the other two methods, which have more sophisticated affecting aspects.

Coupled model verification
After the MPAS-NWW3 model system has been completed constructed, it is necessary to confirm the accuracy of coupled variables transfer and interpolation.In this experiment, we employ a numerical simulation to test the consistency of coupled variables both before and after interpolation.All coupled variables have been tested and verified, including the surface wind at 10 meters above sea level, the temperature and specific humidity at 2 meters above sea level from the atmospheric component model, and the significant wave height, average wave length, and peak frequency from the wave component model.Only the meridional wind component in the atmosphere is shown here due to space restrictions.The variables from MPAS-A are same as it moves to NWW3, as illustrated in Figure 3, indicating that it did not change following the coupler transfer and interpolation.It demonstrates that the coupled variables are interpolated and transferred properly.

Summary
This study presents the development and application of a global atmosphere-wave coupled model with the newly created coupler, C-Couple2.The atmospheric and wave component model in the coupled system is MPAS-Atmosphere and WAVEWATHCH III model, which transfer the coupled variables to another model via the coupler.The coupler also takes on the work of data interpolation between different grids.Consider the influence of wave steepness, wave age or both wave steepness and wave age separately, we introduce three techniques to couple the two component models.The coupled model in this paper applies the wave steepness scheme, that is to say, the influence of the sea surface roughness on the model results is added.
After the coupled model system has been fully established, simulation experiments have been designed and carried out to confirm the consistency of coupled variables both before and after coupling.All coupled variables that exit the component model and enters the coupler are consistent with those that exit the coupler and enter another component model.It demonstrated that the coupled model was accurate.The development of the coupled MPAS-NWW3 model and the functions of coupled variables are the primary foci of this study.It should be noted that just one coupled scheme is tested and discussed in this paper, and the more sophisticated methods would be tested in the future study.

Figure 1 .
Figure 1.The coupling strategy of the global MPAS-NWW3 coupled model.The MPAS-A model sends coupled variables, including surface wind at 10 meters above sea level, temperature and specific humidity at 2 meters above sea level to coupler, and the coupled variables directly drive the wave component model.At the same time, NWW3 sends significant wave height, average wave length and peak frequency back, and MPAS-A receives these coupled variables to calculate an improved sea surface roughness.In this study, only the change in momentum flux brought on by the sea wave is considered in atmospheric model, the heat flux is not taken into account.The coupler is crucial in the coupled model since MPAS-A's mesh structure and domain differ from those of NWW3 model.According to Figure2, each component model's domain is distinct, and the domain of NWW3 is smaller than that in MPAS-A.The C-Coupler2 uses bilinear interpolation (inside the model mesh) and extrapolation (close to the mesh boundary) method to distinguish land and sea distribution.Model mesh structure is the basis of interpolation calculation and variable storage.The exchange of variables between each component model in MPAS-NWW3 coupled system occurs in a two-dimensional horizontal mesh because only variables on sea level are involved.Interpolation between the component models in various mesh structures is the other significant job of coupler.It helps each component model recognize the coupled variables.Additionally, the coupler completes the mesh parallel subdivision to achieve model integration acceleration on high-performance computers.

Figure 2 .
Figure 2. Domain of each component model in coupled MPAS-NWW3 system.(a) is the domain of MPAS-A, (b) is the domain of NWW3.The surface layer scheme in traditional MPAS-A model uses the classic Charnock method to determine the surface roughness[16], whose formula is shown in (1):

Figure 3 .
Figure 3.The meridional wind component (units: m s -1 ) at 10 meters above sea level, (a) is the field in the restart datafile written by the coupler, it is out from the atmospheric component model; (b) is the result of the atmospheric component model; (c) is same as (a), but received by the wave component model; (d) is the discrepancy between (a) and (b).